Extending the work of FrÃ¶hlich, Lue and Furtado-Coelho, we consider the theory of Baer invariants in the context of semi-abelian categories. Several exact sequences, relative to a subfunctor of theâ€¦ (More)

Higher extensions and higher central extensions, which are of importance to non-abelian homological algebra, are studied, and some fundamental properties are proven. As an application, a direct proofâ€¦ (More)

Any semi-abelian category A appears, via the discrete functor, as a full replete reflective subcategory of the semi-abelian category of internal groupoids in A. This allows one to study the homologyâ€¦ (More)

The aim of this paper is to describe Quillen model category structures on the category CatC of internal categories and functors in a given finitely complete category C. Several non-equivalent notionsâ€¦ (More)

Based on the concept of double central extension from categorical Galois theory, we study a notion of commutator which is defined relative to a Birkhoff subcategory B of a semi-abelian category A.â€¦ (More)

Higher dimensional central extensions of groups were introduced by G. Janelidze as particular instances of the abstract notion of covering morphism from categorical Galois theory. More recently, theâ€¦ (More)

A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained,â€¦ (More)

We define relative regular Malâ€™tsev categories and give an overview of conditions which are equivalent to the relative Malâ€™tsev axiom. These include conditions on relations as well as conditions onâ€¦ (More)